Answer
(a) The elevator's upward acceleration is $2.2~m/s^2$
(b) Luke's weight is $784~N$
Work Step by Step
(a) The apparent weight of the box is $1200~N-960~N = 240~N$
We can find the upward acceleration:
$F_N - mg = ma$
$a = \frac{F_N-mg}{m}$
$a = \frac{240~N-(20.0~kg)(9.80~m/s^2)}{20.0~kg}$
$a = 2.2~m/s^2$
The elevator's upward acceleration is $2.2~m/s^2$
(b) We can find Luke's mass:
$F_N - mg = ma$
$F_N = m~(g+a)$
$m = \frac{F_N}{g+a}$
$m = \frac{960~N}{9.80~m/s^2+2.2~m/s^2}$
$m = 80~kg$
Luke's weight is $(80~kg)(9.80~m/s^2) = 784~N$
